The treatment process and operating conditions will affect the relationship. Best studied is activated sludge, assuming that the Monod model is an acceptable representation of the behaviour of the bacteria.
For trickling filter systems you will often find a simple 1st order model was used, resulting in a decaying exponential model against the design parameter - systems depth, or loading rate, or retention time.
Of course, the effluent quality of the treatment plants depends on the organic loads of the influent water and the level of biodegradability of the substances in it. If there are degradable substrates in the influent water and the nutrients are at a sufficient level, then some of the most basic conditions for bacteriological growth have been established. Thus, a high level of purification efficiency can be obtained. In fact, the properties of the inlet water are determined before the treatment plant is installed and the plant is designed accordingly. For example, microbial organisms may be unable to degrade the organic matter in the wastewater, even if the inlet water contains too high COD. In such cases, the BOD5 analysis results may even be zero. Here, substances that are sources of pollution may be xenobiotic or recalcitrance. Hence, it may be necessary to give a detailed answer to your problem. If you give us some more specific information about your work, we can give you more useful information.
In a biological treatment a general equation of biomass production is
x=Y(So-S)
Where x is the concentration of biomass produced, Y is the yield factor (g biomass produced per g substrate utilized), So is the initial substrate concentration and S is the residual substrate concentration. (I have referred herehttp://microbiology.ukzn.ac.za/Libraries/MICR304/MEASUREMENT_AND_KINETICS_OF_MICROBIAL_GROWTH.sflb.ashx)
But on actual wastewater treatment plant you can calculate S (BOD) effluent (which is surely dependent on inlet BOD) by using below calculation
S = So - [(X. HRT. (1+ Kd.SRT)/(Y. SRT)]
Please check. It is the modified equation of 7.43 Metcalf & Eddy.